Topological ordered C- (resp. I-)spaces and generalized metric spaces

Pairwise k-semi-stratifiable bispaces and topological ordered spaces

“…In [15], Künzi 15]). If (X, τ, ) is a topological ordered C-and I-space such that the topology τ is metrizable, is the associated bitopological space (X, τ ♭ , τ ♮ ) quasipseudo-metrizable?…”

“…First, by Theorem 5.3, both (X, τ ♭ ) and (X, τ ♮ ) are γ-spaces. Furthermore, by [15,Theorem 1], (X, τ ♭ , τ ♮ ) is a pairwise stratifiable bispace. Hence, it follows from [20,Theorem 4] that (X, τ ♭ , τ ♮ ) is quasi-pseudo-metrizable.…”

“…Let (X, τ, ) be a topological ordered C-space. It was shown in [15] that if τ is a stratifiable topology, then (X, τ ♭ , τ ♮ ) is pairwise stratifiable. In addition, it was shown in [17] that if τ is a semi-stratifiable (resp.…”

“…An open question posed in [18] is completely solved and results in [2] and [3] are extended to the setting of bitopological spaces. In the last section, we consider the quasi-pseudo-metrizability of a topological ordered spaces and provide a partial affirmative answer to an open problem of Künzi and Mushaandja in [15].…”

On M1- and M3-properties in the setting of ordered topological spaces

“…Proposition. ( [10]) If (X, T, ≤) is a stratifiable ordered topological C-space then the bispace (X, T , T ) is pairwise stratifiable.…”